I'm currently trying to figure out the partial deriviatives of a function, after there is a space transformation.

$$ f(r_1, r_2, w) \rightarrow f(x, y, w)(2\sqrt{xy})^{-1} $$

Where $$ r_1 = x^2 \\ \\ r_2 = y^2 $$

How do I calculate the second partial derivatives, in this new transformed coordinates.

$$ \frac{\partial^2 f(r_1, r_2, w)}{\partial r_1^2}, \ \ \ \ \ \frac{\partial^2 f(r_1, r_2, w)}{\partial r_2^2}, \ \ \ \ \ \frac{\partial^2 f(r_1, r_2, w)}{\partial w^2} $$


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